When I handle a horse's feet there are a couple of things I try to do. I try to always give it back before he takes it. At first I might only be able to hold it for a few seconds but if I never try to force the issue then pretty quickly they learn that it's no big deal and allow me to hold it up longer. If the horse struggles just a little bit in what I call an 'experimenting' way then I might try to hold on until he stops struggling and then set it down and start again. If I think he's going to take it away out of panic though I won't try to hold it.
Another thing I'll do is that when I pick the foot up I get into the working position as smoothly as I can. I'll try to feel the horse's balance and find the most comfortable position for the foot to be in where the horse can stand balanced and comfortable. I'll also make sure that the horse is balanced on all four feet in the first place, before trying to pick a foot up. I believe that one of the biggest reasons that horses snatch their feet away is because people pick the foot up roughly and pull them off-balance. So I'll make sure to avoid doing that if I can.
Sometimes they won't be good about picking up their feet when they're just not wanting to be there or stand still. That's when I'll get them busy doing something else (meaning transitions) until I get the impression that they're ready to stand. I won't even try to pick up their feet unless I'm pretty sure I'll succeed. If the horse is bad about standing and/or their feet this could take all day, but it's worth spending the time if you have it.
Here's a story about one experience I had. I once spent 8 hours with a pony Appaloosa mare who would flip over backwards, even when drugged, when anyone tried to handle her front legs. I'd work with her for 30 minutes, then leave her in the corral and go have a cup of coffee and come back in an hour. I did that all day long, never forced her, and just before the sun went down I got her trimmed. After that one day she would stand to be trimmed with the lead rope draped over her back. That mare really served to show not only how much could be done if I allowed her to be comfortable with the process but how much it was retained even weeks later when the farrier showed up.
That turned out longer than I planned. I can really go all day once I start, but I hope that helps anyway.